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Characterizing the effects of droplines on target acquisition performance on a 3-D perspective display.

INTRODUCTION

Three-dimensional (3-D) displays have potential applications in many areas, such as medicine, aviation, and information visualization (e.g., Ellis & McGreevy, 1983; Gaunt & Gaunt, 1978; Pepper, Smith, & Cole, 1981). Three-dimensional information can be presented on a two-dimensional (2-D) surface by creating head-slaved virtual reality environments, implementing binocular cues that give stereo depth perception, or simply providing monocular visual cues such as linear perspective on a monoscopic display. Linear perspective, a powerful visual cue that has long been used by artists in paintings, has been used more recently in 3-D computer graphics applications. It is a geometric construction in which the appearance (e.g., size) of objects changes as they recede in distance from an observer. Perspective displays, which primarily use linear perspective as a monocular visual cue, have been applied in areas such as aviation (e.g., Ellis, McGreevy, & Hitchcock, 1987). However, in 3-D computer applications in which spatial manipulations are required, transformations along the perspective depth axis are sometimes linked with inaccurate judgments.

Given that 3-D perspective displays are relatively impoverished displays as compared with stereoscopic ones, perspective parameters such as field of view, azimuth, and elevation are always carefully chosen, and supplementary visual cues are often added to the displays to enhance their efficiency (e.g., Barfield, Lim, & Rosenberg, 1990; Barfield & Rosenberg, 1995; Ellis & Hacisalihzade, 1990; Wanger, Ferwerda, & Greenberg, 1992). Ultimately, evaluating the relative efficiencies of variations of 3-D perspective displays and visual cues and understanding how they work have become important issues.

Monocular visual cues such as interposition, shadow, shade, and texture gradient are commonly used in 3-D perspective displays to enhance depth perception. More recently, the dropline has emerged as another useful visual cue. The dropline is a vertical line connecting an object within a 3-D display to an underlying horizontal surface and is meant to enhance information about the relative position of objects in the 3-D space. The dropline can play an important role in 3-D displays. For example, on a 3-D cockpit display of traffic information, many aircraft may be depicted, and it may be difficult to judge the relative positions of aircraft. Note that on such a display, the visual elevation of any aircraft is influenced by both the height of the aircraft and the distance of the aircraft from the nominal viewer position. Therefore, droplines that connect aircraft to the ground surface with lines may help pilots resolve this height/distance ambiguity. Similarly, droplines may be useful in some work domains in which manipulations are relatively close to the eye and the visual context is impoverished. For instance, a 3-D display may not be able to present the positions of objects well enough for manipulations such as those required for endoscopic surgery. In this case, droplines could help a surgeon locate objects more precisely.

Given the potential contributions of droplines on a variety of 3-D display applications, some research has already evaluated the effects of droplines. Visual judgment tasks have been typically used in these evaluations. For instance, Hendrix and Barfield (1997) examined the utility of a perspective display and a stereoscopic display in judgments of the azimuth and elevation separation between two computer-generated cubes. They found that a perspective display and a stereoscopic display resulted in similar performance when a grid plane and droplines were provided on the perspective display. In addition to visual judgment tasks, the effects of droplines also have been examined in terms of manual control performance (e.g., Kim, Ellis, Tyler, Hannaford, & Stark, 1987; Kim, Tendick, & Stark, 1991 ; Park & Woldstad, 2000). Three-dimensional display applications often require visually guided manual responses (e.g., positioning of cursors), and thus examining effects of visual cues on movement performance and navigation strategies is important as well. For example, Kim et al. (1987) found in a manual tracking study that participants performed just as well with the aid of droplines within a perspective display as with a stereoscopic display. A similar study, using pick-and-place tasks (Kim et al., 1991), also showed that a monocular display, with appropriate perspective parameters and droplines, allowed performance equivalent to that on a stereoscopic display.

To date, most studies investigating the effects of droplines on movement performance have focused on continuous tracking tasks, with scant research on how this visual cue affects discrete target acquisition. Target acquisition is a common activity in peoples' daily lives and is becoming more common with increasing use of 3-D applications. It is, therefore, worthwhile to determine if and how droplines benefit target acquisition within a 3-D environment.

Using a 3-D perspective display, the present study examined the effect of droplines on target acquisition performance and strategies. A 3-D perspective reference framework was presented to participants on a computer screen. Participants were asked to use a 3-D input device (a Spaceball) to move a cursor into a target cube as quickly and accurately as possible. The movement trajectory and movement time to acquire the target were recorded and analyzed to test the effects of droplines.

Fitts' Law

Fitts' law, which has been successfully used to describe one- and two-dimensional target acquisition performance, was employed in the present experiment to examine the effects of droplines and to characterize 3-D target acquisition. Fitts (1954) demonstrated a robust linear relationship between the time needed to capture stationary targets and the logarithm of the required relative accuracy in target acquisition tasks. Relative accuracy was measured as the distance from the starting position to the target center, D, divided by half the target width, W/2. The larger this ratio, D/(W/2), the greater the required relative accuracy and the longer the acquisition time. Fitts referred to the logarithm of relative accuracy, [log.sub.2](2D/W), as the index of difficulty (ID). The linear relation between target acquisition time and the index of difficulty is now typically referred to as Flits' law.

Fitts' law and its modified versions (e.g., separating the target distance and width as two individual terms) have successfully characterized target acquisition performance in the physical world and in 2-D human-computer interfaces (see MacKenzie, 1992, for a review/and have also been shown to hold across a wide range of body movements and tasks (e.g., Andres & Hartung, 1989; Crossman & Goodeve, 1965/1983; Drury, 1975; Jagacinski & Monk, 1985: Kerr, 1978; Langolf, Chaffin, & Foulke, 1976). The main merit of Fitts' law stems from its robustness as a quantitative description of target acquisition movements across a variety of movement contexts. Because of such robustness, the law serves as a useful tool for evaluating and comparing human and system performance in different applications.

As 3-D display applications are becoming more popular, how well Fitts' law holds in 3-D target acquisition tasks, and thus how useful it is in evaluating 3-D systems, becomes an important question. Tests of the validity of Fitts' law in a 3-D virtual environment have interested many researchers (e.g., Chung & So, 1999; MacKenzie & Ware, 1993; Ware & Balakrishnan, 1994). For example, MacKenzie and Ware studied the effects of input-output response lag on target acquisition performance in a virtual reality environment. A modified Fitts function was developed in their study to account for the multiplicative effect of the lag and index of difficulty. Chung and So (1999), however, developed a different Fitts model modification to account for the multiplicative effect of the lag and target width in a virtual environment. They suggested that the effects of target distance and width on movement times should be examined separately when there is a lag in a virtual reality system.

Whereas MacKenzie and Ware (1993) and Chung and So (1999) tested only single horizontal axis movements, Ware and Balakrishnan (1994) tested depth movements in and out of the screen in a virtual environment. Like the two aforementioned articles, in the Ware and Balakrishnan experiments the Fitts function was modified to incorporate the head-tracking and hand-tracking system lags, but horizontal movements across the screen and depth movements in and out of the screen were examined separately. They found that depth movements were slightly slower and yielded higher error as compared with horizontal movements. Therefore these studies demonstrated that with some modifications, Fitts' law can be extended to describe target acquisition performance within a 3-D environment.

The present study employed Fitts' law to describe and test the effects of droplines on target acquisition movements within a 3-D perspective display,. In addition to the one-dimensional horizontal and depth movements examined by the aforementioned researchers, vertical screen movements and movements across two and three axes also were examined. Although moving along the depth axis has been found to be more difficult than moving along the other two axes on 3-D displays (e.g., Massimino, Sheridan, & Roseborough, 1989; Werkhoven & Groen, 1998: Zhai & Milgram, 1994; Zhai, Milgram, & Rastogi, 1997), characteristics of display features and visual cues may alter the difficulties of moving along the three axes and across axes. An attempt was made in the present study to utilize Fitts' law to quantitatively capture those differences. For example, on one hand, one ]night expect the slope of the Fitts' law function for depth movements to be steeper than that of the other two axes. On the other hand, it is possible that the use of droplines alleviates this depth axis effect.

Target Acquisition Strategy

In addition to measuring the movement time to acquire targets for Fitts' law analyses, the present experiment also examined participants' dimensional coordinative strategies. The effects of droplines may be revealed by the measure of movement time, but other aspects of movements (such as navigation and movement coordination) may be affected by droplines as well. The present study therefore examined dimensional coordinative strategies in an attempt to reveal any such influences. In the real world, people may typically capture an object along a straight path (the shortest path). However, limitations associated with depth perception, input devices, or display-input device compatibility within a 3-D perspective display may affect how users attempt to capture an object in a 3-D space. Different acquisition strategies may therefore be adopted to compensate for these constraints and to optimize performance. Therefore, the individual acquisitions of each of the three viewer-centered target display dimensions (azimuth, elevation, and range) were examined, and the effects of droplines on the acquisition of those dimensions were investigated.

In summary, the present study attempted to investigate the effects of droplines on target acquisition performance within a 3-D perspective display. Fitts' law was employed to test the effects of interest as well as to capture the differences in moving along the three axes in the 3-D space. Effects of droplines on acquisition movements were further examined from the perspective of coordinative strategy, and the acquisitions of individual viewer-centered target display dimensions were analyzed.

METHOD

The dropline was manipulated as a between-participant variable in the present experiment. Targets were presented at specific spatial locations in a 5-D perspective reference framework (Figure 1) in order to require one-, two-, and three-dimensional movements (movements across one, two, and three axes). As Figure 2 shows, the cursor is located at the origin, and only single-axis movements are needed when the target is located on the horizontal, vertical, or depth axis. Two-axis movements are required when the target is not on an axis but is contained within the horizontal-vertical, horizontal-depth, or vertical-depth plane. Finally, three-axis movements are needed when a target is not located on these planes. In the present experiment, the targets could appear within any of these seven spatial domains (on the horizontal, vertical, or depth axis; within the horizontal-vertical, horizontal-depth, or vertical-depth plane; or not on any axis or plane [3-D location]), and so one-, two-, or three-axis movements could be required to capture a target. Additionally, both target size (W) and target distance (D) from the cursor were manipulated to yield different indices of difficulty [ID = [log.sub.2](2D/W)]. The fundamental dependent variable was movement time.

[FIGURES 1-2 OMITTED]

Participants

Eight participants (4 men, 4 women) participated in the present experiment. They ranged in age from 18 to 52 years. All participants had normal or corrected-to-normal vision, were right-handed, and were paid for their participation.

Stimuli and Apparatus

Participants controlled cursor movements in the 3-D reference framework by manipulating a 3-D input device called a Spaceball (Model 2003, 3D Connexion, Los Gatos, CA). The Spaceball, an isometric input device, is used like a joystick except that the stick is replaced with a ball. The ball senses forces applied in the left-right, up-down, and forward-backward directions and generates corresponding velocities of cursor movements along horizontal, vertical, and depth axes. Because the Spaceball can generate extremely large and fast cursor movements at great force levels, the force was scaled by a 0.10 gain. The Spaceball position was sampled and the display updated at 30 to 50 Hz by a Pentium III computer.

The displayed 3-D reference framework (Figure 1) represented a cubic box of 8.5 inches (21.59 cm) on a side as seen from a nominal 20-inch (50.8-cm) viewing distance (no head restraint was used in the study). At this distance, the front of the reference framework spanned 24[degrees] visual angle vertically and horizontally. The reference framework was shown sitting on a grid surface with grid lines spaced 0.85 inches (2.16 cm) apart in both the horizontal and depth dimensions. The reference framework was tilted 8[degrees] to enhance the perspective view.

The cursor, a small box 0.4 inches (1.02 cm) on a side, always appeared at the center of the reference framework, and a target cube, either 0.8 or 1.2 inches (2.03 or 5.05 cm) on a side, could appear at different spatial locations at the beginning of each trial (Figure 1). The cursor was opaque, colored red in front, and colored green and blue on the sides. The target cube was semitransparent, such that penetration by the cursor could be seen easily. The transparency level of the target cube was manipulated using transparent intensity, an OpenGL graphics parameter that ranges from 0 (fully transparent) to 1 (fully opaque). The target cube had transparent intensity of 0.8 on the back, 0.5 on the front, and 0.6 on the sides. Therefore the brightness of the cursor decreased when it moved within the target and decreased further when the cursor was behind the target. This manipulation of semitransparency was comparable to that of an occlusive cursor cue known as a "silk cursor," which was designed by Zhai, Buxton, and Milgram (1994) for use in a dynamic 3-D target acquisition task.

Droplines were vertical lines extending from both the cursor and the target down to the grid surface, where they terminated in small crosses (Figure 1).

Notice that an additional cue provided in the present experiment caused the target to be highlighted when the cursor was within it. This cue paralleled the cue used by Zhai (1993) in his 3-D object positioning experiments. In those experiments, the stars on the corners of a target (tetrahedron) changed color to indicate a caplure. Finally, the displayed sizes of the target and cursor were automatically scaled by the perspective view. That is, the displayed size of the target and cursor were relatively "larger" when they were closer to the front of the 3-D reference framework than when they were farther away. Therefore the displayed target and cursor sizes could also serve as a depth cue in the present experiment.

Thus several visual cues were been utilized in the present experiment. The droplines were manipulated, and the semitransparency of targets, target highlighting, and scaled visual sizes of the targets and cursor were always available to enhance participants' depth perception and movement performance.

Finally, there were 78 locations where the target could appear in the reference framework: 3 along each of 26 spatial directions (3 x 26 = 78). The 26 spatial directions correspond to bidirectional displacements of the target along 13 lines passing through the initial cursor position (Position b0 in Figure 2). Three of these lines correspond to the horizontal, vertical, and depth axes of the reference framework (Lines b7-b3, a0-c0, and b1-b5, respectively, in Figure 2). Six of these lines correspond to the diagonals of the horizontal-depth, verticaldepth, and horizontal-vertical planes passing through the initial cursor position (i.e., in Figure 2, Lines b8-b4 and b2-b6 in the horizontaldepth plane; Lines a1-c5 and a5-c1 in the vertical-depth plane; and Lines a3-c7 and a7-c3 in the horizontal-vertical plane). The other four lines are not embedded in any of these three planes but connect opposite corners of the framework (i.e., in Figure 2, Lines a8-c4, a2-c6, c8-a4, and c2-a6).

The targets could appear at three distances away from the center along each of the 26 spatial directions. These distances, together with the two target sizes (0.8 and 1.2 inches, or 2.05 and 3.05 cm), yielded six different indices of difficulty. The three distances away from the center for the single axes (horizontal, vertical, and depth) were 1.28, 2.34, and 3.40 inches (3.25, 5.94, and 8.64 cm); for the 2-D planes (horizontal-vertical, horizontal-depth, and vertical-depth) the distances were 1.80, 3.31, and 4.81 inches (4.57, 8.41, and 12.22 cm); and for the 3-D locations the distances were 2.21,4.05, and 5.89 inches (5.61, 10.29, and 14.96 cm). The values of six indices of difficulty for the single axes, 2-D planes, and 3-D locations were therefore 1.00, 1.58, 1.87, 2.42, 2.46, and 3.00; 1.50, 2.08, 2.37, 2.92, 2.96, and 3.50; and 1.79, 2.38, 2.67, 5.21, 3.25, and 3.79, respectively.

Procedure

At the start of the experiment, participants took a seat in front of the computer screen and read instructions about the task. They were then shown examples of the display with targets at different spatial locations. Participants were encouraged to use the Spaceball to move the cursor within the example displays in order to become familiar with the experimental setup. On each trial, the cursor appeared in the center of the display and the target appeared at one of the 78 locations.

Prior to each trial, the participants put their dominant hands on the Spaceball and waited for a "beep" to signal the beginning of the trial. Participants then had to move the cursor into the target cube as quickly and accurately as possible. The target was highlighted once the cursor was moved into the target cube, but the participant had to keep the cursor inside the target for 1 s to complete the trial. The movement time was then displayed on the screen as feedback. The movement time was defined as a duration beginning when the participant started moving the Spaceball and ending when the cursor was moved into the target. There was an intertrial pause of 1 s.

In the present experiment the two target sizes were presented in two separate blocks, such that participants would not incorrectly attribute changes in displayed size to changes in target size. As a result, the variations in perceived target size could be completely attributed to the target distance. Participants received five practice trials before each block of experimental trials. The orders of presenting the big and small target blocks were counterbalanced over participants. Within each block, target location was randomized. Each participant performed five repetitions of the 78 target locations for a total of 390 trials per block. There were breaks halfway through each block and between the two blocks. Participants attended the experiment for two consecutive days. The experiment lasted about 90 min each day. Including practice trials, each participant experienced a total of 790 target acquisitions per day.

Data Analyses

For each trial, Spaceball and cursor positions were sampled every 20 to 30 ms, starting when the cursor and target appeared on the screen and ending when the target acquisition criterion (keeping the cursor within the target for 1 s) was met. Because the Spaceball is a velocity control device, the output cursor positions were an integration of the Spaceball positions. Thus any unsteadiness in the movement of the Spaceball was strongly reduced, given the low-pass filter characteristics of the velocity system.

In addition to analyzing movement time, the present study investigated participants' dimensional coordinative strategy on acquiring targets. That is, the individual acquisitions of each of the three viewer-centered target display dimensions (azimuth, elevation, and range) were examined. This examination was performed by identifying when the target azimuth, elevation, and range dimensions were acquired and then measuring the corresponding movement times associated with each acquisition. For instance, on one hand, a participant could sequentially move the cursor along the three canonical display axes in order to reach a target ("city-block navigation"). This strategy would be reflected, for example, in the sequential captures of target azimuth, elevation, and range. On the other hand, a straight movement across the three axes to reach the target would result in approximately simultaneous acquisitions of the three target display dimensions. Thus the sequence and timing of acquiring the azimuth, elevation, and range dimensions of the target may reflect the participant's sensitivity to the displayed information and, in turn, his or her coordinative strategy. This alternative approach to characterizing target acquisitions allows one to understand participants' coordinative movements in a 3-D space from a different aspect and, additionally, provides a different index of the effect of droplines on coordination movements in the present experiment.

The cursor positions and times at which target azimuth, elevation, and range were acquired were determined by the following procedures. First, visual locations bounding the left, right, top, and bottom of the target perspective view were the boundaries of azimuth and elevation capture regions. The range dimension region of the target was the depth distance (in inches) between the front and back of the target. A computer program was written to first convert the cursor center positions to degrees of visual angle. The program then searched for the respective final times and locations that the cursor center position entered the azimuth and elevation region and, likewise, when and where the cursor center position last entered the range region. Those cursor positions and times corresponded to the azimuth, elevation, and range acquisition events. Figure 3 illustrates the acquisitions of the three target display dimensions.

[FIGURE 3 OMITTED]

The movement times associated with those three acquisitions were measured. Additionally, The temporal order of those three acquisitions was identified in each trial by comparing their associated movement times. For any trial there were 25 different potential sequences that participants could use to acquire the three display dimensions, including those sequences in which two or more dimensions were acquired simultaneously.

RESULTS

Day 1 was considered to consist of practice trials, and data from only Day 2 were analyzed. For each participant, trials with a movement time beyond three standard deviations of his or her average movement time were excluded from the analyses. Overall, about 1.2% of trials were excluded.

The analyses were organized into two parts. The first analysis examined the movement time required to acquire the target and tested Fitts' law. The second analysis examined participants' coordinative strategies, which included analyses of the time to acquire the three target display dimensions, the temporal sequence of acquiring those three dimensions, and the approximately reconstructed movement trajectories. The impact of droplines was of primary interest in those analyses.

Movement Time Analyses and the Test of Fitts' Law

Movement time analyses. The movement times to complete the target acquisitions were examined using analyses of variance (ANOVAs), with dropline as an independent variable. Individual analyses were performed for targets in each of the seven spatial domains (horizontal, vertical, and depth axes; horizontal-vertical, horizontal-depth, and vertical-depth planes; and 3-D locations). Note that the movement times in these analyses were collapsed across different target distances, sizes, and spatial directions within each spatial domain.

Except for the depth axis domain, the mean movement times for the dropline group were generally lower than those for the nondropline group, although the differences for individual domains were not statistically significant (Figure 4). Further analyses were performed to more directly compare performance across the spatial domains. Performance as a function of single-axis spatial domains (horizontal, vertical, and depth) and droplines was analyzed in a 3 x 2 mixed ANOVA, with spatial domain as a within-participant variable and dropline as a between-participant variable. The analysis showed a significant main effect of spatial domain, F(2, 12) = 4.505, p < .05, and a significant Spatial Domain x Dropline interaction, F(2, 12) = 5.72, p < .05. Follow-up analyses were conducted for both the dropline and nondropline groups. There was no significant effect for the nondropline group analysis. However, a significant effect of spatial domain was found for the dropline group analysis, F(2, 6) = 10.28, p < .01. It revealed that both the mean horizontal and mean vertical movement times were significantly lower than the mean depth movement time: M = 1.19 vs. 1.62 s, F(1,5) = 15.25, p<.05, and M = 1.33 vs. 1.62 s, F(1, 3) = 22.03, p < .05, respectively. One can see that the presence of droplines led to poorer performance in the depth domain, and this finding is the opposite of the dropline effect in the other domains.

[FIGURE 4 OMITTED]

Performance as a function of 2-D spatial domains (horizontal-vertical, horizontal-depth, and vertical-depth) and droplines was also analyzed in a 5 x 2 mixed ANOVA. An assumption of sphericity was violated, and therefore a multivariate analysis of variance (MANOVA) was performed. The analysis showed a significant main effect of spatial domain, F(2, 5) = 17.56, p < .01. It revealed that both the mean horizontal-vertical movement time and the mean horizontal-depth movement time were significantly lower than the mean vertical-depth movement time: M = 1.68 vs. 1.97 s, F(1,6) = 7.91,p < .05, and M = 1.78 vs. 1.97 s, F(1, 6) = 37.52, p < .01, respectively.

In summary, the mean movement time for the depth axis was significantly higher than that for the horizontal and vertical axes for the dropline group, but not for the nondropline group. However, the mean horizontal-vertical movement time and the mean horizontal-depth movement time were significantly lower than the mean vertical-depth movement time combining the dropline and nondropline groups.

Test of Fitts' law. Individual regression analyses were performed for each participant for each of the seven spatial domains to test Fitts' law and the effects of droplines. The average [R.sup.2] of all the regressions for the Fitts function (Fitts, 1954) was .71, whereas it was .91 for a modified Fitts function that separates target distance (D) and the inverse of the target width (1/W) as two terms. Therefore, the present data fit the modified Fitts function better than the original Fitts function. The modified Fitts function is

(1) MT = a + b [log.sub.2](D) + c [log.sub.2](1/W).

This modified Fitts function has been used in previous studies within different movement contexts with fairly good fits (e.g., Gan & Hoffmann, 1988; Graham & MacKenzie, 1996; Jagacinski, Repperger; Moran, Ward, & Glass, 1980; Jagacinski, Repperger, Ward, & Moran, 1980; MacKenzie & Graham, 1997).

The resulting [R.sup.2]s varied widely, ranging from .67 to .99 among the 8 participants and the seven spatial domains. Table 1 shows each participant's [R.sup.2]s for regression analyses at the seven spatial domains, and all [R.sup.2]s [greater than or equal to] .90 are noted with asterisks. The average [R.sup.2] of the 56 regressions in Table 1 is .91. Note that most of the relatively low [R.sup.2]s (as low as .67, and with an average of .87) occurred at single-axis spatial domains, especially at the vertical axis. This finding was probably attributable to the low number of replications within the single-axis domain. Because there were only two directions within a single axis, such axes had only two replications for each index of difficulty. These two replications should be contrasted with the eight spatial directions--and thus eight replications--that contributed data to the 3-D location analysis. This 5-D location analysis yielded an average [R.sup.2] of .93. The four directions (four replications) contributing to each of the 2-D plane analyses also yielded an average [R.sup.2] of .93. Finally, notice that the overall goodness of fit does not seem to differ as a function of droplines (mean [R.sup.2] of dropline vs. nondropline = .91 vs. .90).

MacKenzie and Buxton (1992) investigated the extension of Fitts' law to a 2-D task using rectangles as targets. The data were fit to models using different measures of target width, such as the smaller of the rectangle height and width, the width of target along an approach vector, the sum of the height and width, and the area of rectangle. Their results showed a best fit when using the smaller of the rectangle height and width as target width in the model. In the present 3-D display, one may suspect that the target volume could be an alternative for the target width. Note that in the present experiment the target volume is equal to the target width cubed. Given that the logarithm of target volume is equal to three times the logarithm of target width, log([W.sup.3]) = 3logW, substituting target width with target volume will only rescale the parameter c of the modified Fitts function (Equation 1) down by a factor of three and will not change the goodness of fit. Given that the value of parameter c in the present experiment will vary depending on the use of target width or target volume in the equation, the interpretations of the relative importance of parameters b and c (Equation 1) should therefore be more conservative. Unfortunately, the theoretical ramifications are unclear with regard to extending the standard Fitts' law, which applies to one-dimensional size, to the measurement of three dimensions in the present experiment. A potentially profitable future research area would be the examination of this topic.

Target Display Dimensional Coordination Analyses

Display dimensional acquisition time analyses. Acquisitions of the viewer-centered target display dimensions (azimuth, elevation, and range) were also examined, with target display dimension treated as an additional within-participant variable. The results are shown in Figures 5a through 5g. When an assumption of sphericity was violated, individual MANOVAs were performed instead of ANOVAs. Again, the analyses were performed for targets at each of the seven spatial domains.

[FIGURE 5 OMITTED]

A significant main effect of target display dimension was obtained for all seven spatial domains, F(1.061, 6.366) = 55.75, p < .01, F(2, 12) = 228.50, p < .01, F(2, 12) = 222.63, p < .01, F(2, 12) = 47.43, p < .01, F(1.141, 6.849) = 237.83, p < .01, F(1.151, 6.909) = 224.27, p < .01, and F(2, 12) = 254.71, p < .01 for the horizontal, vertical, and depth axes; horizontal-vertical, horizontal-depth, and vertical-depth planes; and 3-D locations, respectively. For targets placed on the three axes, significant differences among the three dimensional acquisition times could be expected because only movements along that axis were necessary. That is, unless participants moved the cursor off of the axis, capture times for the off-axis dimensions would be zero. Figures 5a through 5c show that acquisition times were typically longest for the relevant axis and for range. This effect of range apparently reflects difficulty in maintaining the preexisting alignment of the cursor with the target range but not with target azimuth or elevation.

For targets not aligned with the axes but within one of the relevant planes, significant differences among the three dimensional acquisition times could again be expected because only acquisitions of the two dimensions defined by the plane were needed. As expected, Figures 5d through 5f show that acquisition times were shortest for the dimension not in the relevant plane, with the exception that range capture again remained difficult even when the target was in the horizontal-vertical plane (i.e., the cursor and target were initially at the same range).

For targets at locations where movements along all the three axes were required, a direct cursor movement to the target should result in approximately simultaneous acquisitions of the three target display dimensions. However, the significant main effect of target display dimension obtained for this spatial domain analysis indicated that the three acquisition times were not simultaneous, with range again taking the longest time. Thus participants were not engaging in straight and direct movements.

Significant Dropline x Target Display Dimension interactions were found for targets at all the spatial domains except the depth axis, F(1.061, 6.366) = 8.44, p < .05, F(2, 12) = 29.96, p < .01, F(2, 12) = 23.85, p < .01, F(1.141, 6.849) = 10.04, p < .05, F(1.151, 6.909) = 8.82, p < .05, and F(2, 12) = 50.14, p < .01 for the horizontal and vertical axes; horizontal-vertical, horizontaldepth, and vertical-depth planes; and 3-D locations, respectively. As can be seen, the significant interactions seemed to be primarily attributable to the differences in the range dimension acquisition (Figures 5a, 5b, and 5e) or differences in both elevation and range dimension acquisitions (Figures 5d, 5f, and 5g). Whereas the nondropline group was typically slightly faster for the elevation acquisition, the dropline group acquired the range dimension sooner than the nondropline group did.

Finally, notice that although no depth movements were necessary when the target was located on the horizontal axis, on the vertical axis, or within the horizontal-vertical plane, mean range acquisition time was substantial. The time needed for final range dimension acquisitions in these three spatial domains (Figures 5a, 5b, and 5d) suggests difficulty in judging/maintaining the initial relative depth or range. The interference of horizontal and vertical acquisitions with maintaining alignment may be attributable to visual insensitivity to depth variations caused by Spaceball axis cross-couplings or, perhaps, to physical difficulty in using the Spaceball to control the depth axis. However, depth axis movements were controlled by forward-backward manipulations of the Spaceball, and this is at least as familiar and intuitive as the horizontal left-right Spaceball control axes. Therefore, it is likely that difficulty in depth perception primarily accounts for this interference. The positive effect of the droplines suggests that they may have enhanced depth perception and reduced the depth movement interference to some degree.

Sequence acquisition strategy analyses. As was discussed earlier, different display features, visual cues, or system limitations may have encouraged the adoption of different dimensional acquisition strategies. To gain a better understanding of participants' strategies and whether droplines had any impact on them, the sequence in which the three target display dimensions were acquired in each trial was identified. Including simultaneous acquisitions of dimensions, there were a total of 16 different potential sequences to acquire the three target display dimensions when targets were at the 3-D locations. For targets at the 2-D spatial domains, 16 sequences were still possible, although one dimension (the axis orthogonal to the 2-D plane) was already acquired at the start of the trial. However, because the participant could depart this plane, the capture was not necessarily immediate. Therefore, 6 more potential sequences must also be defined for the 2-D spatial domains to account for cases in which the participant did not depart the plane. The addition of these 6 increased the number of potential sequences to 22 for each 2-D spatial domain. For targets at the single-axis domains, the aforementioned reasoning can be extended and added 3 potential sequences (for a total of 25) for each single-axis spatial domain.

Although there were between 16 and 25 potential sequences across the domains, some sequences were used much more frequently, so only the 5 most frequently used acquiring sequences are reported here. The percentages of trials using those acquiring sequences (collapsed across participants) are plotted for the dropline and nondropline groups and for the seven spatial domains in Figures 6a through 6g. Figures 6a, 6b, and 6d show that although the range dimension acquisition was not necessary for targets on the horizontal axis, on the vertical axis, or within the horizontal-vertical plane, participants lost depth alignment on a substantial number of trials. This finding mirrors the range dimension acquisition times in previous time analyses (Figures 5a, 5b, and 5d).

[FIGURE 6 OMITTED]

However, the dropline group had fewer such trials, again indicating that droplines helped participants reduce this interference with maintaining depth alignment. Notice also that the dropline group acquired range first on a substantial proportion of trials for targets within the vertical-depth plane (and, on a much smaller proportion of trials, within the horizontaldepth plane; Figures 6e and 6f). This finding suggests that participants with droplines had an alternative (but less-preferred) strategy in which they could line up the cursor and the target along the depth axis first and then adjust the cursor along either the horizontal or vertical axis to acquire the target. Finally, note that for targets located at the 3-D locations, range was acquired last for all of the three most frequently used sequences (Figure 6g).

Reconstructions of approximate movement trajectories. In order to better understand the effects of droplines on participants' acquisitions and coordinative strategies, plots of the reconstructed approximate movement trajectories were created for the dropline and nondropline groups for the 2-D and 5-D spatial domains. Figures 7 through 10 represent movement trajectories for the 3-D location, horizontal-vertical, horizontal-depth, and vertical-depth planes, respectively, from different views. These reconstructions were based solely on the trials using the most frequent acquiring sequences in each spatial domain. These approximate movement trajectories were generated by connecting the three acquisition cursor positions averaged across the variations in target size and distance at each dimension and each spatial direction, and across participants in each group.

[FIGURE 7 OMITTED]

The top and bottom panels of Figure 7 show top-down views of the average azimuth-elevationrange sequence acquisitions associated with the four upper and four lower targets at the 3-D locations (toward the eight corners of the reference framework). Each movement trajectory starts from the center cursor position and travels to the pseudo-target positions (averaged positions across the three distance targets). The three consecutive filled circles represent the acquisitions of azimuth, elevation, and range, respectively, and the open squares close to the four corners represent the four pseudo-targets. These sequences account for 45% to 50% of all trials. This figure shows that participants with droplines concurrently moved the cursor in depth, horizontally (azimuth), and vertically (elevation). The nondropline group, however, seemed to leave range adjustments to the end of the movement. Clearly, the participants were better able to coordinate the depth movements with the other two axis movements when droplines were present.

Figures 8, 9, and 10 plot the similar approximate movement trajectories for trials using the most frequent acquiring sequences within the three 2-D planes. Each figure shows reconstructions of acquisitions associated with the four 2-D axis movements within each plane. Figure 8 shows top-down views of movement trajectories for targets on the horizontal-vertical plane that were acquired using an azimuth-elevation-range sequence (34% of all sequences, Figure 6d). Again, the three consecutive filled circles, starting from the center, represent the acquisitions of azimuth, elevation, and range, and the open squares represent pseudo-targets. One can see that on average, depth alignment was lost when participants overlapped the target first. Therefore, they had to adjust the cursor along the depth axis after they overlapped the target.

[FIGURES 8-10 OMITTED]

The most frequent acquiring sequences within the horizontal-depth and vertical-depth planes were azimuth-range (73% of all sequences, Figure 6e) and elevation-range (81% of all sequences, Figure 6f). As can be seen in Figures 9 and 10, compared with acquisitions in the horizontal-vertical plane, there was much less of a tendency to lose alignment in the dimension that was initially captured (i.e., elevation and azimuth, respectively). This tendency again highlights the special difficulty in maintaining depth alignment, as compared with maintaining elevation or azimuth alignment, during cursor movements. In addition, the dropline group was able to make straighter cursor movements, whereas the nondropline group tended to move the cursor along the two axes sequentially. This finding is consistent with a finding discussed previously.

Overall, these reconstructed movement trajectories revealed that droplines helped participants to better coordinate 3-D movements, resulting in straighter and more efficient movements in the 3-D space. Additionally, the presence of droplines highlighted the general tendency of initially overlapping the target with the cursor and then moving the cursor along the line of sight to acquire the target. This therefore suggests that visual information played an important role in the present acquisition task.

To summarize the present results, droplines did not appear to significantly facilitate movement time. In addition, there was not a consistently good fit of the data to a modified Fitts function across all participants for all spatial domains. Moreover; the dropline and nondropline groups did not show any difference in the ability of the data to fit the function. This result makes the interpretation of the data, from the standpoint of Fitts' law, of nebulous value. The analyses of the target display dimensional acquisitions revealed that participants had more trouble acquiring the range dimension or maintaining the range dimension alignment, However, droplines were found to help both target range dimension acquisition and maintenance of the initial relative range dimension alignment. Finally, the approximate movement trajectories illustrated the strategy of visually overlapping the target with the cursor first and then acquiring the target along the line of sight. With droplines, participants were able to better coordinate the depth movements with the horizontal and vertical movements.

DISCUSSION

A goal of the present stud,,, was to examine if and how droplines might facilitate target acquisition performance within a 3-D perspective display. In order to do this, 3-D target acquisition movements were modeled using Fitts' law and using an alternative approach that examined the 3-D coordinative strategies employed by the participants.

Effects of Droplines on Movement Time and Fitts' Law

The droplines showed a relatively consistent, though modest, impact on movement time analyses and did not seem to influence the goodness of fit of the modified Fitts function. Therefore the modified Fitts function may not be an appropriate tool for capturing the effects of perceptual factors such as droplines on 3-D target acquisition performance.

The present 3-D movements may be more variable than the one-dimensional (I-D) movements that are typically associated with the Fitts function, and so good fits were not consistently obtained for regression analyses for all participants and spatial domains. Target acquisition movements within a 3-D space differ from 1-D movements in two important ways: in the degrees of freedom in movements, and in the limitations of depth perception. For example, typical Fitts tasks require simple one-axis movements, and participants typically follow a single direct path. In the present experiment, participants acquired 3-D targets via more articulated and variable movement paths. The target distance parameter, D, therefore did not reflect the actual distances that participants moved. Furthermore, to the extent that participants sequentially captured the targets first by overlapping the 2-D image, and then by capturing the range, the task is best described as two sequential Fitts tasks. The variable movement paths and distances, and the possibility of multiple within-trial dimensional acquisitions, should make the movement time more variable.

In order to try to account for the possibility of articulated paths, further regression analyses were performed. These regressions used participants' actual movement path lengths, instead of Euclidean distance to targets, as the distance term in standard Fitts' law and the modified Fitts function. However, these analyses yielded [R.sup.2]s that accounted for less variance than did those originally obtained using Euclidean distance to target.

Furthermore, in typical Fitts tasks in the physical world, and in those using 2-D computer interfaces, the simplicity of the display ensures that the perceived target distances and sizes unambiguously reflect the real target distances and sizes. Within a 3-D perspective display, however, target size and distance may be ambiguous. Because the accuracy of depth perception in these displays is limited and potentially biased, the perception of a target's distance and size may depend on its depth position. For example, even though target size was blocked and within-block displayed size variations were unambiguous cues to depth variations, participants' acquisition performance may have been influenced by the variations in displayed size. That is, targets located closer to the front of the 3-D reference framework were relatively bigger, whereas targets located toward the back of the 3-D reference framework were relatively smaller. Donkelaar's (1999) experiment showed that pointing movements are affected by size-contrast illusions, thus suggesting the possible influence of size illusions on movements. The variations in displayed target size within the present study therefore may have contributed to the high variability of the data, although this effect may be limited, given that the displayed sizes of near and far targets varied by only around 35%.

Overall, factors from both the movement and perception sides may have contributed to the variability of the data in the present study, and that in turn may have affected the fit of the data to the modified Fitts function. Unfortunately, droplines did not seem to reduce this variability. Future studies may try to investigate individual influences of perceptual and motor factors and determine how Fitts' law can be further modified to take into account those factors. With suitable modifications, Fitts' law may still provide a valuable tool for predicting acquisition performance within 3-D applications.

Droplines and Target Dimensional Coordinative Strategy

The acquiring sequence and movement trajectory analyses showed that the participants utilized a strategy in which they initially overlapped the target with the cursor. Thereafter, they moved along the range dimension, or the line of sight, to acquire the target. Droplines seemed to moderate this strategy; droplines yielded better, but not full, range capture during the initial overlap phase. Participants also appeared to utilize a secondary strategy, which was to initially line up the cursor and target droplines along the depth axis and then to acquire the target along the horizontal or vertical axis (Figures 6e and 6f). However, the overlapping-capturing strategy was a more dominant approach. The dominance of the overlapping-capturing strategy was probably attributable to the fact that visual depth information was the least precise information, even in the presence of droplines.

The lack of binocular depth cues in the present experiment may also have been a major factor in leading participants to use an overlapping-capturing strategy most of the time. Furthermore, the use of the semitransparent targets in the present experiment probably made this strategy easy because once azimuth and elevation were acquired, the semitransparent targets made it easier for participants to monitor and maintain azimuth and elevation alignment as they ranged in on the target depth. Thus, once participants captured azimuth and elevation, they seldom lost them. Finally, many other factors, such as display characteristics, manipulations of input devices, and the task nature, may all have had effects on the strategies participants adopted in performing the task.

Van Erp and Oving (2002) compared target positioning performance differences among the three translational axes within 3-D perspective views by measuring the movement time needed to accomplish the initial 10% error correction. Their data showed relatively much shorter movement times to reach the 10% error correction for the horizontal and vertical axes than for the depth axis. This pattern is therefore comparable with the present finding. The present data showed that acquisition of the azimuth and elevation dimensions was much faster than of the range dimension, and so it could be predicted that the times required to reach the 10% initial error corrections should be relatively shorter for the horizontal and elevation axes than for the depth axis. However, the present study further examined the completion of the three display dimension acquisitions and thus revealed how limitations of depth perception, and depth cuing in the form of droplines, influenced both performance and acquisition strategies.

The present experiment demonstrated that droplines particularly benefit acquisitions of the target range dimension. For target acquisitions that required depth movements, participants who had droplines were able to acquire the target range dimension sooner than participants who did not. For acquisitions that did not require depth movements, vertical or horizontal movements appeared to interfere less with maintaining depth alignment when participants had droplines. Moreover, with the depth information provided by droplines, participants were better able to simultaneously move and coordinate the cursor along the three axes. That is, they could move the cursor via straighter and more efficient paths to acquire the targets.

Cao, MacKenzie, and Payandeh (1996) compared expert and novice surgeons' performance in laparoscopic surgery by decomposing basic surgical tasks into subtasks and component motions. One of their findings was that although reaching and grasping are typically performed in parallel when performing goal-directed prehension movements (Jeannerod, 1984), the saint movement components were performed in series in laparoscopic surgery. It was suggested that performing motions one at a time may be a way to minimize the maneuvering constraints in the operative field by reducing the degrees of freedom. Therefore, constraints in laparoscopic surgery resulted in additional information processing demands on the surgeons, and thus the motions that they normally executed in parallel in nature were now planned and executed serially. The present results revealed a similar effect. That is, when there were no droplines, participants were constrained by insufficient depth information and so tended to navigate the front-parallel plane first, followed by the range dimension. However, when droplines were provided and they had better perception of depth information, they were able to navigate in the 3-D space more naturally and so could perform simultaneous maneuvers along three axes.

Finally, it is important to note that the present strategies were reliably (consistently) associated with particular participants. When the data from the practice session (Day 1) and the data from the session used for the experimental analyses (Day 2) were compared, the comparison showed very similar results on the 2 days, demonstrating that individual participants' 3-D acquisition strategies were relatively reliable, or consistent. On a practical level, however, one may be interested in knowing whether there was an association between the participants' acquisition strategies and their performance. Specifically, some participants' strategies may have resulted in performance that was better than those of others. An examination revealed no systematic relation between strategies and performance. Therefore, the results of the present experiment do not suggest any advantage in training operators on any particular acquisition strategy. However, the fact that droplines resulted in a strategy with a shorter navigation path but no significant change in movement time suggests that using the droplines was not without cost. The slower movement speed suggests that using the droplines might have required enough of the participants' attention to offset any gains attributable to shorter path length. Thus more practice may be needed for participants to use droplines in a more automatic manner without costing attention resources.

Target Acquisitions Among Different Spatial Domains

Some additional observations regarding movements in the 3-D space are in order. Depth axis movements have been previously shown to be the most difficult. The Massimino et al. (1989) continuous tracking task with velocity and acceleration controllers showed that error along the depth axis was higher than that along the horizontal and vertical axes. Other studies with continuous tracking tasks showed that error along the horizontal axis was lower than that along the vertical axis, which, in turn, was lower than that along the depth axis (Zhai & Milgram, 1994; Zhai et al., 1997). However, in the present study only the dropline group had significantly greater movement time for the single depth axis movements, and overall the single depth axis movements were not shown to be significantly more difficult than the single horizontal and vertical axis movements (Figure 4). Moving along the depth axis therefore may not always be more difficult than moving along the other two axes, and it may depend on different factors, such as 3-D display characteristics, input device, and task nature.

The poorer movements for the vertical and vertical-depth domains may be attributed to how visual information for vertical location (height) and depth location (distance) covary in perspective scenes (i.e., objects farther away, but below eye level, tend to be higher in the visual field). Therefore the visual results of moving the cursor up and down along the vertical axis and back and forth along the depth axis may be confused with each another. The confounding of the cursor vertical and depth distance changes may have made vertical and/or depth target acquisitions more difficult. Difficulty in acquiring the vertical axis may also be attributed to difficulties in using the heave (up-down) dimension of the Spaceball. That is, vertical movements of the cursor required lifting up and pushing down the Spaceball, and these are not common manipulations in most input devices.

In a part of Van Erp and Oving's (2002) study that examined continuous tracking performance, they found in 5-D perspective views that tracking errors for up-down movements were about 10% larger than for the fore-aft axis. This difference in error was present regardless of the different display-control mappings manipulated in their experiment. A motor system effect was suggested for this movement asymmetry. Zhai et al. (1997), in their six-dimensional continuous tracking task, also found that vertical errors were nearly as large as depth errors early in practice, although they dropped close to the size of horizontal errors later in the experiment. Although the present study analyzed only the data from Day 2, it is possible that performance on the vertical movements required more practice in order to be comparable to that of the horizontal movements.

Conclusions

As 3-D perspective displays have been broadly applied to different areas, a need to evaluate their efficiencies has increased. Although using visual judgment tasks is an effective method for evaluating the benefits of cuing in 3-D perspective displays, the present study has shown that examining the effects of visual cues on users' movement performance is also important. The present study evaluated the effect of a visual cue dropline on target acquisition performance within a 3-D perspective display. Performance was evaluated by Fitts' law, and coordinative strategies within a 3-D space were examined by examining the acquisitions of each target display dimension.

Detailed analyses of acquisitions of the target display dimensions and movement trajectories were most illuminating. They revealed that droplines benefited acquisition of the target range dimension and altered the coordination of movements along the three axes. These analyses also revealed that a dominant strategy, which participants adopted across both the dropline and nondropline conditions, was to visually overlap the cursor with the target first and then acquire the target along the depth axis of the line of sight. The present study suggests that droplines have potential in enhancing efficiencies of coordinative movements and target acquisition performance in an interactive 3-D perspective display. However, the data in the present study were too variable to show consistently good fits to the modified Fitts function across all participants and all spatial domains. Whether the data would better fit the function changes with practice or whether they reveal a limitation in the applicability of Fitts functions to acquisitions using perspective displays remains to be determined.
TABLE 1: [R.sub.2] of the Regression Analyses for the Seven Spatial
Domains for the Eight Participants

                             Dropline Group

Horizontal            .86     .83     .70     .99 *
Vertical              .99 *   .92 *   .99 *   .74
Depth                 .96 *   .97 *   .73     .94 *
Horizontal-vertical   .87     .88     .88     .96 *
Horizontal-depth      .97 *   .95 *   .84     .98 *
Vertical-depth        .96 *   .94 *   .88     .96 *
3-D locations         .98 *   .92 *   .97 *   .99 *

                            Nondropline Group

Horizontal            .82     .91 *   .98 *   .90 *
Vertical              .69     .67     .89     .89
Depth                 .93 *   .96 *   .99 *   .73
Horizontal-vertical   .94 *   .97 *   .87     .96 *
Horizontal-depth      .98 *   .94 *   .95 *   .94 *
Vertical-depth        .81     .99 *   .95 *   .96 *
3-D locations         .87     .79     .99 *   .97 *

* [R.sub.2] a .90.


ACKNOWLEDGMENTS

This work was performed while the first author held a National Research Council (NASA/ Ames Research Center) research associateship. The authors wish to thank Dr. Robert Welch, Dr. Kevin Jordan, Dr. Doreen Comerford, and the two anonymous reviewers for their helpful comments.

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Date received: November 29, 2001

Date accepted: January 13, 2004

Min-Ju Liao is a research associate at the San Jose State University Foundation. She received her Ph.D. in cognitive/experimental psychology from the Ohio State University in 1997.

Walter W. Johnson is a research psychologist at NASA Ames Research Center. He received his Ph.D. in cognitive/experimental psychology from the Ohio State University in 1986.

Address correspondence to Min-Ju Liao, NASA Ames Research Center, Mail Stop 262-2, Moffett Field, CA 94035-1000; mliao@mail.arc.nasa.gov.
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Title Annotation:Displays And Controls
Author:Liao, Min-Ju; Johnson, Walter W.
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Date:Sep 22, 2004
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